Robust stability conditions for feedback interconnections of distributed-parameter negative imaginary systems
Khong, Sei Zhen LU ; Petersen, Ian R. and Rantzer, Anders LU
(2018)
In Automatica
90.
p.310-316
- Abstract
Sufficient and necessary conditions for the stability of positive feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint (IQC) approach. The IQC framework accommodates distributed-parameter systems with irrational transfer function representations, while generalising existing results in the literature and allowing exploitation of flexibility at zero and infinite frequencies to reduce conservatism in the analysis. The main results manifest the important property that the negative imaginariness of systems gives rise to a certain form of IQCs on positive frequencies that are bounded away from zero and infinity. Two additional sets of IQCs on the DC and instantaneous gains of the systems are... (More)
Sufficient and necessary conditions for the stability of positive feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint (IQC) approach. The IQC framework accommodates distributed-parameter systems with irrational transfer function representations, while generalising existing results in the literature and allowing exploitation of flexibility at zero and infinite frequencies to reduce conservatism in the analysis. The main results manifest the important property that the negative imaginariness of systems gives rise to a certain form of IQCs on positive frequencies that are bounded away from zero and infinity. Two additional sets of IQCs on the DC and instantaneous gains of the systems are shown to be sufficient and necessary for closed-loop stability along a homotopy of systems.
(Less)
- author
- Khong, Sei Zhen
LU
; Petersen, Ian R.
and Rantzer, Anders
LU
- organization
- publishing date
- 2018-04-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Distributed-parameter systems, Integral quadratic constraints, Negative imaginary systems, Robust feedback stability
- in
- Automatica
- volume
- 90
- pages
- 7 pages
- publisher
- Pergamon Press Ltd.
- external identifiers
-
- scopus:85041481692
- ISSN
- 0005-1098
- DOI
- 10.1016/j.automatica.2017.09.010
- language
- English
- LU publication?
- yes
- id
- e72b6397-8892-4a31-8d7c-f308b5fa7266
- date added to LUP
- 2018-02-20 10:33:22
- date last changed
- 2023-11-17 14:09:13
@article{e72b6397-8892-4a31-8d7c-f308b5fa7266,
abstract = {{<p>Sufficient and necessary conditions for the stability of positive feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint (IQC) approach. The IQC framework accommodates distributed-parameter systems with irrational transfer function representations, while generalising existing results in the literature and allowing exploitation of flexibility at zero and infinite frequencies to reduce conservatism in the analysis. The main results manifest the important property that the negative imaginariness of systems gives rise to a certain form of IQCs on positive frequencies that are bounded away from zero and infinity. Two additional sets of IQCs on the DC and instantaneous gains of the systems are shown to be sufficient and necessary for closed-loop stability along a homotopy of systems.</p>}},
author = {{Khong, Sei Zhen and Petersen, Ian R. and Rantzer, Anders}},
issn = {{0005-1098}},
keywords = {{Distributed-parameter systems; Integral quadratic constraints; Negative imaginary systems; Robust feedback stability}},
language = {{eng}},
month = {{04}},
pages = {{310--316}},
publisher = {{Pergamon Press Ltd.}},
series = {{Automatica}},
title = {{Robust stability conditions for feedback interconnections of distributed-parameter negative imaginary systems}},
url = {{http://dx.doi.org/10.1016/j.automatica.2017.09.010}},
doi = {{10.1016/j.automatica.2017.09.010}},
volume = {{90}},
year = {{2018}},
}